number obtained by interchanging the digits of a two digit number is less than the original by 18 and the sum of the digit ia 6. what is the original number ?
To find the original number, we need to set up an equation based on the given information.
Let's assume the original two-digit number is represented by "10x + y", where x and y are the digits in the tens and units places, respectively.
According to the problem, the number obtained by interchanging the digits is "10y + x". And we are told that this number is less than the original by 18. Therefore, we can set up the equation:
10y + x = 10x + y - 18
Next, we are given that the sum of the digits is 6. So we can set up another equation:
x + y = 6
Now, we have a system of two equations:
Equation 1: 10y + x = 10x + y - 18
Equation 2: x + y = 6
We can solve this system of equations to find the values of x and y, which will give us the original number.
Subtracting x and y from both sides of Equation 1, we get:
10y - y = 10x - x - 18
9y = 9x - 18
Dividing both sides by 9, we have:
y = x - 2
Now we substitute this expression for y in Equation 2:
x + (x - 2) = 6
2x - 2 = 6
Add 2 to both sides:
2x = 8
Divide both sides by 2:
x = 4
Now we can substitute the value of x back into Equation 2 to find y:
4 + y = 6
y = 6 - 4
y = 2
So the original number is 42.